{"id":"https://openalex.org/W2997798549","doi":"https://doi.org/10.1109/access.2019.2961191","title":"On Mixed Metric Dimension of Rotationally Symmetric Graphs","display_name":"On Mixed Metric Dimension of Rotationally Symmetric Graphs","publication_year":2019,"publication_date":"2019-12-23","ids":{"openalex":"https://openalex.org/W2997798549","doi":"https://doi.org/10.1109/access.2019.2961191","mag":"2997798549"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2961191","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2961191","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08937516.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08937516.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050403373","display_name":"Hassan Raza","orcid":"https://orcid.org/0000-0002-1477-3608"},"institutions":[{"id":"https://openalex.org/I148128674","display_name":"University of Shanghai for Science and Technology","ror":"https://ror.org/00ay9v204","country_code":"CN","type":"education","lineage":["https://openalex.org/I148128674"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hassan Raza","raw_affiliation_strings":["Business School, University of Shanghai for Science and Technology, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-1477-3608","affiliations":[{"raw_affiliation_string":"Business School, University of Shanghai for Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I148128674"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076981458","display_name":"Jia\u2010Bao Liu","orcid":"https://orcid.org/0000-0002-9620-7692"},"institutions":[{"id":"https://openalex.org/I118987531","display_name":"Anhui Jianzhu University","ror":"https://ror.org/0108wjw08","country_code":"CN","type":"education","lineage":["https://openalex.org/I118987531"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jia-Bao Liu","raw_affiliation_strings":["School of Mathematics and Physics, Anhui Jianzhu University, Hefei, China"],"raw_orcid":"https://orcid.org/0000-0002-9620-7692","affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Anhui Jianzhu University, Hefei, China","institution_ids":["https://openalex.org/I118987531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055101551","display_name":"Shaojian Qu","orcid":"https://orcid.org/0000-0002-4746-270X"},"institutions":[{"id":"https://openalex.org/I148128674","display_name":"University of Shanghai for Science and Technology","ror":"https://ror.org/00ay9v204","country_code":"CN","type":"education","lineage":["https://openalex.org/I148128674"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shaojian Qu","raw_affiliation_strings":["Business School, University of Shanghai for Science and Technology, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-4746-270X","affiliations":[{"raw_affiliation_string":"Business School, University of Shanghai for Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I148128674"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":5.7843,"has_fulltext":true,"cited_by_count":44,"citation_normalized_percentile":{"value":0.96608358,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"8","issue":null,"first_page":"11560","last_page":"11569"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9373000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6157981753349304},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6112695932388306},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5985915660858154},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5631700754165649},{"id":"https://openalex.org/keywords/metric-dimension","display_name":"Metric dimension","score":0.49920129776000977},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4878113567829132},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.358364462852478},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3251921236515045},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31525859236717224},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17446520924568176},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.0606708824634552}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6157981753349304},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6112695932388306},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5985915660858154},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5631700754165649},{"id":"https://openalex.org/C60933471","wikidata":"https://www.wikidata.org/wiki/Q17152964","display_name":"Metric dimension","level":5,"score":0.49920129776000977},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4878113567829132},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.358364462852478},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3251921236515045},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31525859236717224},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17446520924568176},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.0606708824634552},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2961191","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2961191","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08937516.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:457b233cd209491ea8059ceb76613c78","is_oa":true,"landing_page_url":"https://doaj.org/article/457b233cd209491ea8059ceb76613c78","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 8, Pp 11560-11569 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2961191","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2961191","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/08937516.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2199675829","display_name":null,"funder_award_id":"1701081B","funder_id":"https://openalex.org/F4320335473","funder_display_name":"Postdoctoral Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G3065972664","display_name":null,"funder_award_id":"11601006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3218190166","display_name":null,"funder_award_id":"2017M621579","funder_id":"https://openalex.org/F4320335473","funder_display_name":"Postdoctoral Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G4760238211","display_name":null,"funder_award_id":"5B19303001","funder_id":"https://openalex.org/F4320324854","funder_display_name":"University of Shanghai for Science and Technology"},{"id":"https://openalex.org/G7765875064","display_name":null,"funder_award_id":"1701081B","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G828030330","display_name":null,"funder_award_id":"2017M621579","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G950439790","display_name":"\u591a\u76ee\u6807\u9c81\u68d2\u51f8\u89c4\u5212\u95ee\u9898\uff1a\u7406\u8bba\u3001\u7b97\u6cd5\u548c\u5e94\u7528\u7814\u7a76","funder_award_id":"71571055","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320324854","display_name":"University of Shanghai for Science and Technology","ror":"https://ror.org/00ay9v204"},{"id":"https://openalex.org/F4320335473","display_name":"Postdoctoral Science Foundation of Jiangsu Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2997798549.pdf","grobid_xml":"https://content.openalex.org/works/W2997798549.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W133470447","https://openalex.org/W2026014023","https://openalex.org/W2037298352","https://openalex.org/W2074389465","https://openalex.org/W2083763715","https://openalex.org/W2108442028","https://openalex.org/W2112641412","https://openalex.org/W2802116907","https://openalex.org/W2811210202","https://openalex.org/W2899421048","https://openalex.org/W2903472770","https://openalex.org/W2916524213","https://openalex.org/W2952434773","https://openalex.org/W2963118757","https://openalex.org/W2966255984","https://openalex.org/W2970222247","https://openalex.org/W2970441787","https://openalex.org/W2978678889","https://openalex.org/W2982597716","https://openalex.org/W3100731361","https://openalex.org/W6676813938","https://openalex.org/W6755118912","https://openalex.org/W6769498025"],"related_works":["https://openalex.org/W2561539344","https://openalex.org/W1758702617","https://openalex.org/W2955893777","https://openalex.org/W2321819494","https://openalex.org/W2362685149","https://openalex.org/W2936559436","https://openalex.org/W4379057405","https://openalex.org/W4287690335","https://openalex.org/W2895230703","https://openalex.org/W3133002653"],"abstract_inverted_index":{"A":[0,33,120],"vertex":[1,68],"u":[2],"\u2208":[3,16],"V(G)":[4],"resolves":[5],"(distinguish":[6],"or":[7,12],"recognize)":[8],"two":[9,56],"elements":[10,58],"(vertices":[11,59],"edges)":[13,61],"v,":[14],"w":[15],"E(G)UV(G)":[17],"if":[18,54],"d":[19,26],"<sub":[20,27,36,72,97,116,121,127,140,145,149,155,159,165,178,182,188,192,205],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[21,28,37,73,98,117,122,128,141,146,150,156,160,166,179,183,189,193,206],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">G</sub>":[22,29],"(u,":[23,30],"v)":[24],"\u2260":[25],"w)":[31],".":[32,75],"subset":[34],"L":[35,71],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</sub>":[38,74,99,147,180],"of":[39,62,70,79,113],"vertices":[40],"in":[41],"a":[42,48,80],"connected":[43],"graph":[44,203],"G":[45,53,63,85],"is":[46,86,93,171,198],"called":[47,87],"mixed":[49,81,89,107,209],"metric":[50,82,90,108,210],"generator":[51,83],"for":[52,84,110,138,174],"every":[55],"distinct":[57],"and":[60,92,125,173,200],"are":[64],"resolved":[65],"by":[66,95],"some":[67],"set":[69],"The":[76,202],"minimum":[77],"cardinality":[78],"the":[88,106,133,143,176],"dimension":[91,109,211],"denoted":[94],"dim":[96,144,154,177,187],"(G).":[100],"In":[101],"this":[102],"paper,":[103],"we":[104],"studied":[105],"three":[111],"families":[112],"graphs":[114],"D":[115,139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[118,123,129,142,151,161,167,184,194,207],",":[119,124,130],"R":[126,204],"known":[131],"from":[132],"literature.":[134],"We":[135],"proved":[136],"that,":[137],"(D":[148,158],")":[152,162,185],"=":[153,163,186],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">e</sub>":[157,190],"dim(D":[164],"),":[168,195],"when":[169,196],"n":[170,197],"even,":[172],"An":[175],"(A":[181,191],"even":[199],"odd.":[201],"has":[208],"5.":[212]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":4}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}